Problem: Solve for $x$ and $y$ using elimination. ${6x+2y = 34}$ ${-5x-2y = -30}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the top and bottom equations together. ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {6x+2y = 34}\thinspace$ to find $y$ ${6}{(4)}{ + 2y = 34}$ $24+2y = 34$ $24{-24} + 2y = 34{-24}$ $2y = 10$ $\dfrac{2y}{{2}} = \dfrac{10}{{2}}$ ${y = 5}$ You can also plug ${x = 4}$ into $\thinspace {-5x-2y = -30}\thinspace$ and get the same answer for $y$ : ${-5}{(4)}{ - 2y = -30}$ ${y = 5}$